particle moving on a cardioid at constant frequency
This is another elementary example11C.F. particle moving on the astroid at constant frequency about particle kinematics. In this case we will use polar coordinates. Let us consider the cardioid 22the locus of the points of the plane described by a circle (or disc) boundary point which it is rolling over another one with the same radius .
with given constants and means time parameter. The position vector of a particle, respect to an orthonormal reference basis moving on the cardioid is
and its velocity 44in polar coordinates we have because the base vectors are changing on direction and sense according the formulas We are using the chain rule with Overdot denotes time differentiation everywhere.
Therefore the speed is
and the tangent vector
Next we use the formula
and by using the time derivative of base vectors
getting the equation
|Title||particle moving on a cardioid at constant frequency|
|Date of creation||2013-03-22 17:14:20|
|Last modified on||2013-03-22 17:14:20|
|Last modified by||perucho (2192)|